Question

A 4-foot long steel pipe consists of two concentric cylinders, with the inner cylinder hollowed out. The radius of the outside of the pipe is 6 inches and the radius of the inside of the pipe is 5.75 inches.

HINT: The units of measure must be the same! Convert to inches and keep your answer in terms of π.
A. Determine the volume of metal used to build the pipe.
B. If the pipe is to be powder-coated on the inside and outside surfaces, what is the total surface area to be powder-coated?

Answer 1

volume of metal =
`141 \pi\ inch^(3)`

Surface area of cylinder to be powder-coated=
`1133.875\pi\ inch^(2)`

Explanation:

Radius of outer circle, R = 6 inch

Radius of inner circle, r = 5.75 inch

Height of cylinder, h = 4 ft = 4 * 12 inch = 48 inch

Calculating the volume of metal used to build this pipe:

`\text{Volume of hollow cylinder} = \pi R^(2)h - \pi r^(2)h`

`\Rightarrow \pi 48(6^(2) - 5.75^(2))\\\Rightarrow \pi 48(2.9375)\\\Rightarrow 141 \pi\ inch^(3)`

Inner and outer surfaces are to be powder-coated.

Total surface area = Lateral surface area + Area of solid bases

`\Rightarrow 2\pi Rh + 2 \pi rh + 2(\pi R^(2) - \pi r^(2))`

`\Rightarrow 2\pi * 48 (6 + 5.75) + 2\pi(6^(2) - 5.75^(2))\\\Rightarrow \pi (96 * 11.75 + 2.9375 * 2)\\\Rightarrow 1133.875 \pi\ inch^(2)`

So, volume of metal =
`141 \pi inch^(3)`

Surface area of cylinder to be powder-coated=
`1133.875 \pi\ inch^(2)`